The generator matrix

 1  0  1
 0  1  X
 0  0  1

generates a code of length 3 over Z2[X]/(X^2) who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+6x^1+15x^2+20x^3+15x^4+6x^5+1x^6

The gray image is a linear code over GF(2) with n=6, k=6 and d=1.
As d=1 is an upper bound for linear (6,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 6.51e-005 seconds.